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AACE International Exam CCP Topic 4 Question 22 Discussion
Topic #: 4
A used concrete pumping truck can be purchased for $125,000. The operation costs are expected to be $65,000 the first year and increase 5% each year thereafter. As a result of the purchase, the company will see an increase in income of $100,000 the first year and 5% more each subsequent year. The company uses straight-line depreciation. The truck will have a useful life of five (5) years and no salvage value. Management would like to see a 10% return on any investment. The company's tax rate is 28%.
Assuming the average life span of a lithium battery is two years and is normally distributed with a standard deviation of two months, what is the probability the battery will last between 20 months and 26 months?
Given that the average life span of the lithium battery is 24 months with a standard deviation of 2 months, we need to calculate the probability that the battery will last between 20 and 26 months.
Using the Z-score formula:
Z=XZ = \frac{X - \mu}{\sigma}Z=X
For 20 months: Z=20242=2Z = \frac{20 - 24}{2} = -2Z=22024=2
For 26 months: Z=26242=1Z = \frac{26 - 24}{2} = 1Z=22624=1
Looking up these Z-scores in the standard normal distribution table:
Z = -2 corresponds to approximately 2.28%
Z = 1 corresponds to approximately 84.13%
The probability that the battery will last between 20 and 26 months is approximately 84%.
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